document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=326720>Question 326720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I found out that a fraction of : (7x+1)/(x+1)(x-2) simplifies as follows : <BR>\n" );
document.write( "2/(x+1) + 5/(x-2)\r<BR>\n" );
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document.write( "Could you please guide me as to how I can simplify similar fractions? Is it based solely on experience or is there some kind of methodology? I would be really grateful if you'd help me on this!\r<BR>\n" );
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document.write( "Sincerely yours,<BR>\n" );
document.write( "Kollias Panos </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233939 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using partial fractions we have<BR>\n" );
document.write( "(7x + 1)/[(x + 1)(x - 2)] = A/(x + 1) + B/(x - 2)\r<BR>\n" );
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document.write( "Multiply throughout by (x + 1)(x - 2) gives<BR>\n" );
document.write( "7x + 1 = A(x - 2) + B(x + 1)\r<BR>\n" );
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document.write( "By putting x=2 we can eliminate A and get<BR>\n" );
document.write( "7(2) + 1 = A(2 - 2) + B(2 + 1)<BR>\n" );
document.write( "15 = 3B<BR>\n" );
document.write( "B = 5\r<BR>\n" );
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document.write( "Similarly by putting x=-1 we can eliminate B and get<BR>\n" );
document.write( "7(-1) + 1 = A(-1 - 2) + B(-1 + 1)<BR>\n" );
document.write( "-6 = -3A<BR>\n" );
document.write( "A = 2\r<BR>\n" );
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document.write( "Therefore (7x + 1)/[(x + 1)(x - 2)] = 2/(x + 1) + 5/(x - 2)\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "(7x + 1)/[(x + 1)(x - 2)] = [2(x - 2) + 5/(x + 1)]/[(x + 1)(x - 2)]\r<BR>\n" );
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document.write( "(2x - 4 + 5x + 5)/[ (x + 1)(x - 2)] = (7x + 1)/[(x + 1)(x - 2)]\r<BR>\n" );
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document.write( "So using this example should enable you to work out other fractions like this using this method.<BR>\n" );
document.write( "It is a bit more difficult for repeated factors and factors of higher orders but for the moment we will stick to non-repeated linear factors.<BR>\n" );
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